Method and Device for Characterisation of Multiple Samples of One or Various Dispersions

ABSTRACT

The invention relates to a method and a device for the automatic determination of selected physical and colloidal chemistry parameters (for example, the grain size, the distribution of grain sizes, the hindrance function and indices of structural stability) by means of the determination of the attenuation of radiated waves through monodisperse or polydisperse dispersion samples subjected to gravitation or centrifugation, characterised in that during the segregation by means of centrifugation or gravitation, the instantaneous transmission I T (t, r) characterising the current segregation status of the waves radiated with the intensity I o (t, r) and/or the instantaneous scattering I S (t, r) as a function of the position within the samples is repeatedly determined and recorded at high resolution at any arbitrary time for one or more wavelengths over the entire length of the sample or in selected partial sections of it, simultaneously for multiple and even concentrated samples with known and/or unknown physical and colloidal chemistry properties.

The characterisation of fluid-fluid or fluid-solid dispersions, forexample with respect to segregational stability and structuralstability, as well as the separation behavior in the centrifugal field,is an important task in research, the design of (large) technicalseparation processes, the development of new products, as well as inquality control close to the production line. The grain size, as well asthe distribution of grain sizes, plays a special role here. Ideally,this is to be surveyed without dilution, which means in the originalstate, because changing the composition can also lead to changes in themeasured size (dilution agglomeration, for example).

There are a number of different measurement methods known, which aredistinguished with respect to the physical measurement procedure, thearea of application (for example, concentration of the same, range ofgrain sizes) as well as the measurement options (for example,resolution, type of size distribution, measurement accuracy) (Allan, T.:Particle Size Measurement, Kluwer Academic Publishers, Netherlands(1999)/Leschonski, K.: Particle measurement technology, report from theBunsen Company for Physical Chemistry, (1984)). Regardless of whetherfractionated or non-fractionated measurement techniques are involved,all instruments used up until now allow the determination of the grainsize of only one sample. In other words, multiple samples must always bemeasured one after the other. First, this is costly in terms of timebecause the samples to be measured are often away from the measurementchamber, the chamber must be washed and dried, and the next sample mustbe poured in. Second, the samples are not measured under identicalconditions (for example, temperature drift, subjective andhardware-caused settings particularities, erroneous settings, electronicnoise level). Third, a validation of the instruments and/or themeasurement for a reference sample is not possible in parallel, whichmeans simultaneously with the actual measurement. In addition, common toall known methods is that various substance parameters (for example,viscosity of the dispersion medium, optical constants) for the samplesto be analysed must be known even for diluted samples, in order to beable to calculate a distribution of grain sizes from the measurementresults evaluated based on volume. For concentrated dispersions,additional particle-particle interaction effects and particle-fluidinteraction effects are to be taken into consideration, such as theincreasing substance-specific hydrodynamic interaction (hindrancefunction) that is non-linear with the volume concentration, for example.This substance characteristic is of importance for high-resolutionfractionated measurement methods in particular.

Until now, the sample-specific data had to be compiled through previoustests of the sample both with rheologic and optical measurement methods,and prepared in a suitable manner, for example using special input menusfor the respective analysis procedures for the determination of grainsizes. The entire procedural chain is very costly in terms of time, istainted by measurement errors and cannot be automated. It also proves tobe particularly limiting that the predominant majority of the grain sizemeasurement methods can only be used for diluted or even highly-dilutedsubstance samples. For this reason, many micro-dispersions andnano-dispersions cannot be measured under conditions that are close tothe product.

Although fractionated measurement methods are distinguished fromnon-fractionated methods (for example, static or dynamic lightscattering) by a significantly higher resolution, in particular forpolymodal samples, the previous technical solutions realized arecharacterised by a series of inadequacies. The following fractionatedmeasurement methods are currently known for dispersions: Gravitysedimentation methods, centrifugal field sedimentation methods (disccentrifuges, photo cuvette centrifuges and manometer centrifuges)

Disc centrifuges are laboratory devices with a sample chamber in theform of a disc, which is accelerated to between 600 and 24,000revolutions per minute⁻¹ (CPS Instruments, Inc. USA,http://www.cpsinstruments.com/ Brookhaven Instruments Corporation USA,http://www.bic.com). When the specified final speed is reached, thesuspension to be analysed is introduced onto the surface of a fluid thatwas poured into the sample chamber in advance. In principle, the sampleis quite heavily diluted by doing so. In addition, hydrodynamicinstabilities often occur when “immersing” the particles into thespinning fluid. This leads to starting times and starting speeds thatare tainted with errors. Since the temperature of the measurementchambers cannot be maintained, a calibration measurement for determiningthe current base value must first be established by means of referenceparticles for the thickness and viscosity of the spinning fluid, whichare dependent on the temperature. In principle, this involves the riskof impurity from the displacement of reference particles into the sampleto be subsequently applied.

As a result of the centrifugal force, the particles begin to migrateoutwards according to their size. A suitable source of radiation ispositioned such that the disc is X-rayed at a position determined by themanufacturer, for the most part at the outside edge. Through scatteringand absorption, the sedimenting particles reduce the intensity of theradiation, which is measured by a receiver at a constant position. Fromthe time elapsed and the particle migration and the measurement of theattenuated radiation intensity, the size and the concentration of theparticles are determined. Disc centrifuges are in the position to detectparticles in the range of sizes from 0.01 μm to 40 μm. The samplethroughput is limited by the fact that only one sample can be measuredin each case.

Known photo cuvette centrifuges likewise measure the opacity of a lightbeam or laser beam only for one sample and at one level (ShimadzuScientific Instruments (SSI) North America: http://www.ssi.shimadzu.com/Horiba: http://www.horiba-particle.com/). In contrast to the disccentrifuges, the particles are evenly dispersed in a transparent cuvetteat the start of the test. As a result of the centrifugal acceleration,the particles begin to sediment and pass the light cabinet according totheir membership in individual size classes. For this reason, theopacity decreases with time, and the particle size distribution can becalculated from this temporal transmission increase and the associatedsink speed.

A measurement of the particle concentration by means of a detectionmethod for electromagnetic radiation forms the basis of both methods,the disc centrifuge and the photo cuvette centrifuge. Corresponding tothe prior art, radiation sources are used in the visible range for thedetermination of the particle size distribution. The extinctioncoefficients that depend on particle size corresponding to the MieTheory are required for a calculation of the particle size distributionevaluated on the basis of volume or mass (van de Hulst, H. C.: LightScattering by Small Particles, Dover Publications Inc., New York(1981)/Kerker, Milton: The scattering of light and other electromagneticradiation, Academic Press, New York, San Francisco, London, (1967)).

If X-ray radiation is used, absorption coefficients that depend onparticle size can be used. However, in addition to the technicalradiation safety aspects, this has the disadvantage that only sampleswith materials of higher atomic numbers (typically>13) can be measured.Biological samples, for example, cannot be analysed for this reason.

In order to test the sedimentation behavior that is dependent on grainsizes for particles in the centrifugal field, a manometer centrifuge canbe used, whose principle is based on the measurement of the hydrodynamicdifference in pressure between two measurement levels in a sedimentationcell (Beiser, M., Stahl, W.: Influence of Additives on the SedimentationBehaviour of Fine Grained Solids in the Centrifugal Field, FiltechEurope 2003—Conference Proceedings, Volume I-L-Session, pageI-465-I-472). When a solid substance that has a higher density than thefluid precipitates out, the average mass density of the suspensionvolume between the two measurement levels decreases continuously, andthe hydrodynamic difference in pressure likewise reduces as a result.The process continues until the separation level between the clearliquid and the sedimentation zone has passed the lower measurementlevel. If all particles sink at the same speed, a linear distribution ofthe hydrodynamic difference in pressure in terms of time results.However, if there are particles in the suspension that sediment rapidlyand slowly, the change in pressure is initially made up of both parts,and if the particles sinking more rapidly have abandoned the measurementvolume, the slope of the pressure curve changes. If n particle classesare present in the suspension, n-1 inflexion points result in thetemporal pressure curve, or an arched curve for a constant particle sizedistribution. Information about the sedimentation mechanisms can bederived from these pressure curves, i.e. at what concentrations thetransition between zone and cluster sedimentation lies, for example. Alarge disadvantage is the costly measurement of the pressure in therotating sedimentation cell and the transfer of the temporal pressurecurve during the centrifugation. Even here, only one sample can betested during a measurement.

In addition, it is common for the technical devices for the previouslydescribed centrifugation method to be targeted to the measurement ofsuspensions. If anything, a modification must be made for themeasurement of emulsions. Mixed dispersions (milk products, for example)that exhibit simultaneous flotation and sedimentation segregation inprinciple could not be analysed with this method with respect to grainsize without prior separation.

In the European patent specification EP 0 840 887 B1, a method and adevice for the automatic analysis of geometric, mechanical andrheological parameters of substance systems and materials is described,which is based on the different cuvettes or measurement systems matchedto the tested commodity and the test parameter(s), which are also placedin different positions radially, being placed on a carriage or rotorpositioned horizontally or vertically, and being subjected to atime-variable acceleration that is preset or controlled depending on thecourse of the process. The change in the local and temporal compositionof the substance system induced by the acceleration, the geometricarrangement or position of the materials, or the position of thecorresponding sample specimen is detected with high resolution by meansof mechanical or electromagnetic waves. Multiple materialcharacteristics—such as segregation speed, flotation speed, viscosity,viscoelasticity, concentration by volume, distribution of grain sizes,particle types, elasticity, adhesion, adhesiveness or tensilestrength—as well as their time dependencies are calculated online oroffline simultaneously from these signals using appropriate algorithms.

The subject matter of the patent applications DE 102 08 707.5-52 A1 andEP 1 386 135 A2 is a method and a device, with which both the stabilityor instability of a dispersion can be measured, or with whichstabilising or destabilising effects on a dispersion can be tested. Atthe same time, the instantaneous measurement of the local composition ofthe dispersion is made possible with high local and temporal resolutionusing the overall level of the measurement cells as well as theirtemporal change in intervals of a hundredth of a second without movementof measurement cell, transmitter or receiver in relation to one another.

Likewise, for the multi-channel devices from the patent specificationsEP 0840887 B1, DE 102 08 707.5-52 A1 and EP 1 386 135 A2, thetransmission is recorded, solved in terms of location and time without atemperature option (exception patent specifications DE 102 08 707.5-52A1 and EP 1 386 135 A2) for the samples. Until now, it has provenparticularly disadvantageous here that the transmission signal wasrecorded only as a virtual, device-dependent intensity, and that themethod extended primarily to the ascertainment of the particle-freesolution/dispersion boundary layer. A conversion of the transmittedintensity into extinction values proportional to concentration was notprovided either for dilute or for undiluted dispersions in particular.Also lacking are appropriate mathematical algorithms that make possiblethe simultaneous experimental determination of the grain sizes of asample and the substance-specific characteristics (for example,size-rated extinction coefficients, hindrance or flux density functionthat depend on concentration) required for the calculation of thesesizes using the multi-channel capability under the same measurementconditions and with the same measurement values. An automaticsoftware-based analysis and documentation of these characteristics wasnot provided.

The object of the invention is based on the elimination of thedisadvantages of the solutions described in the prior art.

The object is achieved according to the invention in that, by means of aspectroscopic measurement device functioning in a linear range (lightsource, condenser, line receiver), the attenuation caused by theparticles of the dispersion (for example through absorption and/orscattering) is ascertained with respect to the radiated intensity ofwaves of one or more wavelengths. The scattered intensity can bedetected alternatively or simultaneously. The transmitted and/orscattered intensity is determined, stored and analysed over the entireextent of the sample, resolved for both location and time. The developedalgorithms make possible the analysis according to the invention of theextinction changes at different selectable locations in the measurementsample depending on the time, or as a function of the position withinthe measurement sample for different selectable times. At the same time,it is particularly advantageous that the corresponding determination ofthe analysis mode as well as the corresponding locations and times musttake place only during the analysis after the experiment, and can berevised with arbitrary frequency, and thus even highly complexdispersions (suspoemulsions, for example) are to be analysed easily. Ithas also proven advantageous that, in addition to the samples withunknown grain size distributions to be analysed, simultaneous referencesamples with different volume concentrations and/or known grain sizedistributions are carried out at the same time, and from the results forthe reference samples acquired under identical measurement conditions,the optical parameters indispensable for the determination of the grainsize distribution for the unknown samples as well as the hindrance andflux function (function for the description of the transport in terms ofthe cross section) in the case of concentrated samples can becalculated. Surprisingly, it turned out that the solution according tothe invention also made it possible to determine the relative apparentviscosity as a function of the particle concentration as well assubstance-specific parameters for rheologic equations.

The equipment for the method according to the invention makes possiblethe segregation of 12 different samples in the gravitation orcentrifugal field, for example, and the detection of the dischargedintensity I_(T)(t, r) over the entire length of the sample by means of aCCD line as a receiver matched to the wavelength (880 nm, for example;others are possible) of the radiation source, for example. The range ofobservation can be extended by shifting a CCD line or other suitablepunctiform sensors gradually along the cuvettes. With respect to theknown disc and photo cuvette centrifuges, the discovered solution alsomakes possible the use of optical path lengths to the cuvettescoordinated to the starting opacity, and the variation of the radiatedintensity. The measurement of concentrated samples can also be realisedby doing so. The entire spectroscopic measurement device as well as thesamples are maintained at a temperature of from 4° C. to 60° C., forexample, during the measurement for achieving the required analysisaccuracy. It also arose that the method according to the invention isnot in the position to analyse floating substance systems like emulsionsin terms of selected physical and colloidal chemistry parameters withoutchanges to the measurement apparatus, but surprisingly even mixturesystems that contain particles with more limited and greater densitiesthan the suspension medium can be characterised without separation bygrain sizes in advance.

The method according to the invention and the device according to theinvention make it possible for the first time to automatically determineselected physical and colloidal chemistry parameters (for example, thegrain size, the distribution of grain sizes, the hindrance function(function that describes the deviation of the sedimentation behaviorfrom the Stokes law) and indices of structural stability (differentcharacteristics for structural stability, for example flow limits) fordispersion samples through the determination of the spatially andtemporally resolved impairment of radiated waves through themonodisperse or polydisperse dispersion samples subject to gravitationor centrifugation (dispersions with uniform or deviating particlesizes). It should be analogously applicable without prior separation forfloating (creaming) and sedimenting substance systems, as well as formixtures of them.

The method according to the invention for the automatic determination ofselected physical, technical method and colloidal chemistry parameters(for example, the grain size, the distribution of grain sizes, the speeddistribution, the particle flux (particle transport related tocross-section), the hindrance function and indices of structuralstability) takes place by means of the determination of the attenuationof radiated waves during the segregation of monodisperse or polydispersedispersion samples subjected to gravitation or centrifugation, andincludes the following steps/partial steps:

-   -   During the centrifugation, the instantaneous transmission        I_(T)(t, r) characterising the current segregation status of the        waves radiated with the intensity I_(o)(t, r) is repeatedly        determined and recorded at high resolution at any arbitrary time        for one or more wavelengths over the entire length of the sample        or in selected partial sections of it, simultaneously for        multiple and even concentrated samples with known and/or unknown        physical and colloidal chemistry properties. Alternatively or at        the same time, in addition to the transmission, the        instantaneous scattering I_(S)(t, r) can hereby be determined        and recorded as a function of the position within the samples.        The characterisation of the dispersion samples can also take        place without centrifugation.    -   The extinction profile E_(T)(t, r) is calculated by finding the        log of the ratio of I_(o)(t, r)/I_(T)(t, r) as a basis for the        determination of the particle or droplet concentration for the        tested dispersion samples as a function of sample position and        time.    -   From these extinction profiles E_(T)(t, r) determined at        different times (t1 . . . tn) and the local adjustment made in        these time segments (t(n−1)−t(n)), segregation speeds are        calculated for any constant extinction values.    -   From the ratio of the segregation speeds determined for specific        extinction percentiles, a polydispersity index (measure of the        breadth of the distribution) is calculated, which is        characteristic for the polydispersity of the density or the        particle or droplet size.    -   Extinction-weighted distributions of the grain size are        calculated from extinction profiles E_(T)(t, r) for selectable        times according to Equation A (see below) while standardising on        the maximum extinction for this profile. As a supplement        thereto, the local and temporal change of the particle or        droplet concentration can be determined, taking into account the        substance-specific extinction-concentration relationship.    -   The determination of the substance-specific        extinction-concentration relationship through the simultaneous        segregation of samples of the substance system to be measured        can be carried out with known, varying volume concentrations,        whereby the concentration effect on the extinction is calculated        while taking into account the repeated scattering, for example        according to Equation B (see below).    -   From any extinction profiles acquired at time t, the        volume-weighted distributions of the grain size are calculated        according to Equations A and C (see below). The volume-specific        extinction cross section that is dependent on particle size and        that is required for doing so (extinction cross section: area on        which the same energy falls from the radiation as is masked        through absorption and scattering) is calculated according to        Mie from the known optical substance parameters and including        the device constants. As an alternative to this, the method        allows the experimental determination of the volume-specific        extinction cross section that is dependent on particle size, if        the extinction is determined from at least two monodisperse        reference samples.    -   As an alternative to this, the method allows the experimental        determination of the volume-specific extinction cross section        that is dependent on particle size, if the course of the        extinction is determined during the segregation of at least one        polydisperse substance system with similar optical        characteristics.    -   Using the volume-weighted particle size distribution specified        above, the particle size dependency for the volume-specific        extinction cross sections determined above, and the        concentration-dependent extinction determined, each radial        position and the particle size associated with it via Equation A        is associated with a concentration by volume corresponding to        Equation D (see below).    -   The flux density function (Equation F—see below) standardised to        the centrifugation constant is determined from the change in the        concentration of the samples with a known starting        concentration. Corresponding to Equations E, E* and F, the        concentration-dependent hindrance function for the substance        system can be determined.    -   The volume-weighted distribution of the Stokes equivalent        diameter for the case of hindrance functions not equal to 1 is        determined by iteratively repeating Equation G instead of        Equation A for the steps mentioned above until the differences        between the steps following one another for the concentration        profiles are less than a value to be provided in advance, or if        the allowance for the hydrodynamic impediment (Equation E) is        provided by means of another suitable mathematical algorithm,        for example via the definition of a cost function.    -   The determination of the grain sizes and their distribution for        dispersed particles is possible with density both greater and        less than that of the dispersion medium.

In place of the position-dependent extinction profile E_(T)(t, r) attime t, the extinction is determined as a function at a freelyselectable position or over a range (r+δr) of the sample, and thedistribution of grain sizes is calculated from it analogously to theabove calculation.

The apparent relative viscosity can be calculated as a function of theconcentration by volume from the determined hindrance function, takinginto account the concentration by volume.

The sedimentation type and the critical concentration by volume for theuse of consolidation phenomena can be determined from the change in thesegregation speed during the segregation.

The ascertainable range of the distribution of sizes as well as theresolution with respect to the distribution of grain sizes can beincreased by varying the number of revolutions and the measurement timeintervals.

The mass density distribution of the sample is calculated from theextinction profile E_(T)(t, r) for a known distribution of grain sizes.

For mixtures of substances of different densities, the distribution ofgrain sizes for the individual substance components is calculated fromthe extinction profiles for the segregation of dispersions withdifferent densities for the dispersion medium.

For mixtures of substances of different densities, the distribution ofgrain sizes for the individual substance components is calculated fromthe extinction profiles for the segregation of dispersions withdifferent densities for the dispersion medium.

Indices for the consolidation behavior of the dispersion samples can becomputed from the sediment levels for gradually changed revolutionsrelated to the respective operative centrifugal force.

The control of the segregation analyser and the measurement sensor,including radiation source, sample management and data transfer, datahandling and data storage, as well as all steps of analysis and thedocumentation of the results, takes place by means of software supportedby a database.

The device according to the invention for the automatic determination ofselected physical, technical process and colloidal chemistry parameters(for example, the grain size, the distribution of grain sizes, the speeddistribution, the particle flux, the hindrance function and of indicesof structural stability) consists of a PC-controlled multi-samplereceptacle unit arranged vertically or horizontally with a spectrometricmeasurement device with a source producing monochromatic parallelradiation, which registers, digitises and stores the radiation intensityscattered or transmitted by the respective dispersion sample over theentire length of the sample simultaneously or shifted temporally duringthe segregation, resolved for location and time.

Different cuvettes matched to the measurement task and/or the dispersionsample with respect to the optical path length and the materials can beused; the cuvette type is detected automatically, and the parametersrequired for the analysis of the measurement results are automaticallymade available via database entries for the calculation of theparameters to be analysed.

Radiation sources of different monochromatic wavelengths, whoseradiation intensity I_(o)(t, r) can be varied, are also used electivelyin an alternating fashion, depending on the sample and measurementtasks.

The measurement range can be controlled by thermostat, and themeasurements can be carried out both above and below room temperature atselectable temperatures.

The multi-sample receptacle unit is designed as a rotor, and is drivenby a motor with programmable variable and/or constant revolutions. As analternative to this, the device according to the invention has amulti-sample receptacle unit, which makes it possible to receive samplesplaced vertically for segregation in the gravitational field.

The features of the invention develop not only from the claims but fromthe description as well, whereby the individual features in each caserepresent advantageous embodiments that are subject to protection, aloneor together in the form of combinations, for which protection is appliedfor with this document. The combination consists of known elements(ascertainment of the attenuation of radiated waves during thesegregation of monodisperse or polydisperse dispersion samples subjectedto gravitation or centrifugation) and new elements (determination of theparameters through the specified calculation principles), which interactand provide an advantage in their new overall effect (synergisticeffect) and the desired result, which is due to the fact that now, forthe first time, selected physical and colloidal chemistry parameters(for example, the grain size, the distribution of grain sizes, thehindrance function and indices of structural stability) can bedetermined automatically for dispersion samples through theascertainment of the spatially and temporally resolved attenuation ofradiation waves through the monodisperse or polydisperse dispersionsamples subject to gravitation or centrifugation.

The invention is to be explained in greater detail on the basis ofexemplary embodiments without being limited to these examples.

EXEMPLARY EMBODIMENT 1 Calculation of the Distribution of Grain Sizesfor Known Optical Parameters

From the light intensity from the light source I₀(t), which can be set,and the intensity that is detected by the sensor for a particularposition in the sample, a location profile is determined for thetransmission I_(T)(t, r) or the scattering I_(S)(t, r), and thecorresponding extinction profile E_(T)(t, r) is determined after findingthe log of the ratio I₀(t) to I_(T)(t, r). If the measurement isrepeated at different times, it is possible to observe the temporalprogress of the sedimentation at the base of the cuvette for a suspendedsolid substance that has a greater density than the fluid, and tocalculate the distribution of grain sizes from that. The followingexemplary equations are used to do so (other types of functions areabsolutely possible)

$\begin{matrix}{{x\left( {r,t} \right)} = \sqrt{\frac{18 \cdot \mu_{C}}{\left( {\rho_{P} - \rho_{F}} \right) \cdot \omega^{2} \cdot t} \cdot {\ln \left( \frac{r}{r_{0}} \right)}}} & \left( {{Equation}\mspace{14mu} A} \right) \\{{E\left( {A_{V},c_{V}} \right)} = {A_{V} \cdot c_{V} \cdot L \cdot \left\lbrack {1 - {{EXP}\left( {a + \frac{b_{1}}{A_{V} \cdot c_{V}} + \frac{b_{2}}{A_{V}^{2} \cdot c_{V}}} \right)}} \right\rbrack}} & \left( {{Equation}\mspace{14mu} B} \right) \\{{Q_{3}\left( {x\left( {r,t} \right)} \right)} = \frac{\int_{E_{\min}}^{E{(r)}}{\frac{r^{2}}{A_{V}\left( {x\left( {r,t} \right)} \right)}\ {{E(r)}}}}{\int_{E_{\min}}^{E_{\max}}{\frac{r^{2}}{A_{V}\left( {x\left( {r,t} \right)} \right)}\ {{E(r)}}}}} & \left( {{Equation}\mspace{14mu} C} \right) \\{{c_{V}\left( {r,t} \right)} = {{c_{V,{ges}} \cdot {Q_{3}\left( {x\left( {r,t} \right)} \right)}} = \frac{E\left( {r,t} \right)}{\begin{matrix}{{Q_{3}\left( {r,t} \right)} \cdot {\int_{0}^{\infty}\left\lbrack {{A_{V}\left( {x\left( {r,t} \right)} \right)} \cdot} \right.}} \\{\left. {q_{3}\left( {x\left( {r,t} \right)} \right)} \right\rbrack \ {x}}\end{matrix}}}} & \left( {{Equation}\mspace{14mu} D} \right) \\{{\mu \left( {c_{V}\left( {r,t} \right)} \right)} = \frac{\mu_{app}\left( {c_{V}\left( {r,t} \right)} \right)}{\mu_{C}}} & \left( {{Equation}\mspace{14mu} E^{*}} \right) \\{{\Phi \left( {c_{V}\left( {r,t} \right)} \right)} = \frac{{c_{V}\left( {r,t} \right)} \cdot \left( {1 - {c_{V}\left( {r,t} \right)}} \right)^{2}}{\mu \left( {c_{V}\left( {r,t} \right)} \right)}} & \left( {{Equation}\mspace{14mu} F} \right) \\{{\eta \left( {c_{V}\left( {r,t} \right)} \right)} = {\frac{v}{v_{Stokes}} = \frac{\left( {1 - {c_{V}\left( {r,t} \right)}} \right)^{2}}{\mu \left( {c_{V}\left( {r,t} \right)} \right)}}} & \left( {{Equation}\mspace{14mu} E} \right) \\{{x\left( {r,t} \right)} = \sqrt{\frac{18 \cdot \mu_{C}}{\left( {\rho_{P} - \rho_{F}} \right) \cdot \omega^{2} \cdot t \cdot {\eta \left( {c_{V}\left( {r,t} \right)} \right)}} \cdot {\ln \left( \frac{r}{r_{0}} \right)}}} & \left( {{Equation}\mspace{14mu} G} \right)\end{matrix}$

EXEMPLARY EMBODIMENT 2 Determination of the Distribution of ParticleSizes for Sediment Samples, Ascertainment of the Extinction Coefficientsfrom the Course of the Extinction for a Sample of Known Distribution

In the example, the distribution of particle sizes was determined on thebasis of the segregation kinetics of 2 sediment samples (fraction<63μm).

Reference measurement: The distribution of grain sizes was determined bymeans of a reference method (sedimentation in the normal gravitationalfield, detection by means of X-ray absorption, radiation attenuationproportional to the mass concentration). The ascertained distribution isto be gathered from Table 1.

TABLE 1 Results from the Sedigraph measurements (spherical shapeassumption, particle density 2.65 g/cm³) m % < m % < m % < m % < m % < m% < Sample 2 μm 10 μm 16 μm 20 μm 50 μm 63 μm A 56.1 92.4 97.1 98.7 99.399.1 B 64.7 95.3 99.6 100.3 101.1 100.6

Preparation of samples: In the first step, the sediment samples werediluted to a concentration of approximately 1 m % by adding thedispersing agent sodium pyrophosphate (0.13 m %). These dispersions werethen mixed with sugar for calibrating a favorable viscosity such thataqueous dispersions with approximately 0.5% solid substance is presentin 50% sugar solution.

The sediment dispersions were treated for 15 minutes 3 times in anultrasonic bath in order to achieve the most complete dispersion anddegasification.

Experiment: The centrifugal analysis was performed with 12 samples atthe same time (6 parallel determinations in each case) using plasticcuvettes with a film thickness of approximately 2.2 mm with a rotorspeed of a constant 500 revolutions per minute. Sample A served as areference sample, which means the known distribution for this sample wasused for the determination of the dependency of the extinctioncoefficients on the particle size. This dependency was used in order tocalculate the distribution of particle sizes for Sample B from themeasurement results, and to compare them with the results of thereference measurement for Sample B.

The determination of cumulative distribution of particle sizes wasperformed on the basis of the ascertainment of the mass fraction for theparticle fraction, which had already precipitated out of the samplecompletely at the different points in time at which the transmission wasmeasured. The temporal course of the transmission averaged over therotor position from 106.5 to 107.5 mm was used for the analysis. Thisposition was 6 mm above the bottom of the cuvette.

The diameter of the particle x, which had all already passed rotorposition 107 mm at the time of the measurement, was calculated on thebasis of Equation H:

$\begin{matrix}{x^{2} = {\frac{18 \cdot \mu_{C}}{\Delta \; {\rho \cdot \omega^{2} \cdot t}} \cdot {\ln \left( \frac{r}{r_{0}} \right)}}} & \left( {{Equation}\mspace{14mu} H} \right)\end{matrix}$

with:

-   -   Δρ Difference in the density between dispersed substance and        dispersion medium    -   μ_(c) Viscosity of the dispersion medium    -   ω Angular speed    -   R₀ Radial position of the fill level    -   R_(A) Average radial position for the transmission analysis

It was calculated with the values for μ_(c)=15 mPa s, Δρ=1.4 g/cm³ (samesample density that serves as the basis for the reference measurement).

A conversion of the measured transmission values T (%) into extinctionvalues E_(T)(t, R_(A)) is necessary for the data analysis. Theexperimentally determined transmission values for the samples are to becorrected advantageously according to Equation I with respect to thetransmission of the cuvettes T_(cell) (empty value) filled with thedispersion medium. One obtains the temporal change for the extinction inthe range from 106.5 to 107.5.

$\begin{matrix}{{E_{T}\left( {t,R_{A}} \right)} = {- {\ln \left( \frac{T\left( {t,R_{A}} \right)}{T_{cell}\left( {t,R_{A}} \right)} \right)}}} & \left( {{Equation}\mspace{14mu} I} \right)\end{matrix}$

The changes to the extinction correspond to the change in the localparticle concentration, which is caused by the particle fraction thatprecipitated out (Equation H).

The temporal course of the extinction E_(T)(t, R_(A)) was used in orderto calculate, by means of the extrapolation of the extinction startingvalue E_(T)(0, R_(A)), which

original concentration and size distribution the tested samplecorresponds to.

In an initial approximation, the cumulative distribution of particlesizes (uncorrected values) can be estimated from the temporal course ofthe relative extinction change E_(rel)=E_(T)(t, R_(A))/E_(T)(0, R_(A)).E_(T)(0, R_(A)) corresponds to the uppermost threshold value for thedistribution at a diameter of 63 μm (cumulative−100% m/m) and a valuefor E_(rel)=1. E_(rel) corresponds, in a rough approximation, to thecumulative mass fraction for the particles that are smaller than theparticles that have already precipitated out completely (Equation H).

In this case, the information about the starting concentration is notnecessary, but the dependency of the extinction coefficients on theparticle size is neglected.

In the example provided, this dependency was calculated with a knowndistribution of sizes from the simultaneously determined course of theextinction for Sample A. The following steps were necessary for thispurpose.

From the information on the cumulative distribution of particle sizesfor Sample A for the mass fraction of particles smaller than 2, 10, 16,20, 50 and 63 μm, a distribution function % m/m=f(d [μm]) wasrecalculated by means of the equalising function

$\begin{matrix}{y = {\frac{a}{\left( {1 + \frac{x}{x_{0}^{b}}} \right)}.}} & \left( {{Equation}\mspace{14mu} J} \right)\end{matrix}$

Other equalising functions can be used as well.

The range of particle sizes between 1.5 and 63 μm ascertained via themeasurement was split into sub-fractions. The extinction coefficientswere determined for these sub-fractions by comparing the changes in themass fractions corresponding to Equation J with the change in theextinction (E_(T)(t, R_(A))) in this range.

The equalising function

y=y ₀ +a·x+b·x ² +c·x ³  (Equation K)

with:

-   -   y—Extinction coefficient    -   x—Particle diameter        that was computed from this extinction coefficients is shown in        FIG. 1 for Sample A.

This equalising function was used with the ascertained parameters inorder to determine the distribution of particle sizes for Sample B fromthe measurement data from the analytical centrifugation.

The range of the particle sizes was in turn split into sub-ranges forthis purpose. Its concentration was calculated on the basis of EquationK from the relative change in the extinction and the respectiveextinction coefficients (corresponding to the average values for theparticle diameter for the sub-range). The cumulative distribution ofparticle sizes then results from the mass concentration of the startingsample and the mass concentration of the sub-fractions.

The distribution function determined in this manner for Sample B (emptysymbols) shows very good agreement with the results from the referencemeasurement (filled symbols, see FIG. 2).

It can therefore be concluded that for samples that are similar to oneanother, a routine determination of the distribution of grain sizes ispossible according to the described method without prior knowledge ofthe extinction coefficients.

EXEMPLARY EMBODIMENT 3 Determination of the Hindrance and Flux DensityFunction for a Monodisperse Silicon Dioxide Sample

In this example, the hindrance function was determined on the basis ofthe segregation kinetics of a monodisperse silicon dioxide suspensionwith a particle size of 550 nm.

Preparation of samples: For the determination of the hindrance functionand thus the measurement of a dilution sequence, a concentrated startingsuspension of approximately 15% by volume was prepared and diluted tothe desired concentrations (10, 5, 4, 3, 2, 1, 0.85, 0.65, 0.5, 0.4,0.3, 0.2 and 0.1% by volume). The dispersion of the starting suspensionwas performed as follows.

First, the powder was stirred in deionised water with a magneticstirrer. In a second step, the suspension was treated for 15 minutes ineach case with a high-speed disperser based on the rotor/statorprinciple until the distribution of particle sizes (measurement withlaser diffraction) no longer changed. Then the suspension was furtherdispersed with an ultrasonic dispersion apparatus in pulse mode. Thisprocess was likewise repeated until the distribution of particle sizesdid not change. Finally, the pH value was adjusted to the value of 8 byadding 0.1 M KOH, and the solid substance concentration was measuredwith a thermal scale. The individual dilution stages were produced fromthe starting suspension with deionised water and treated in theultrasonic bath for 5 minutes prior to the test in order to ensurecomplete dispersion and degasification.

Experiment: The centrifugal analysis was performed with 8 samples threetimes and 4 samples once at the same time (4 and 2 paralleldeterminations for controls in each case) using plastic cuvettes with afilm thickness of approximately 2.2 mm with a rotor speed of a constant2000 revolutions per minute.

The determination of the hindrance function was carried out on the basisof the ascertainment of the sink speeds v from the segregation kinetics,in which the position of the phase boundary between fluid free of solidsubstance and suspension was applied over the time for each dilutionstage. The increase in the resulting segregation curve is the averagemeasured sedimentation speed. This was then divided by the theoreticalStokes sink speed (Equation E and Equation L).

$\begin{matrix}{v_{Stokes} = \frac{\left( {\rho_{P} - \rho_{F}} \right) \cdot x \cdot r \cdot \omega^{2}}{18 \cdot \mu_{c}}} & \left( {{Equation}\mspace{14mu} L} \right)\end{matrix}$

with:

-   -   ρ_(P) Density of the dispersed substance 2.0 g/cm³    -   ρ_(F) Density of the dispersion medium 0.994 g/cm³    -   μc Viscosity of the dispersion medium 0.722 mPa s    -   x Particle size    -   ω Angular speed 209 l/s    -   r Average position ( (R₀+R_(a))/2)

So that the hindrance function is available for concentrations otherthan those tested experimentally, the concentration dependency for themeasured sink speeds in terms of the Stokes was adjusted exemplarily tothe following function (Equation M) with the least squares method.

$\begin{matrix}{\eta = {\frac{v}{v_{Stokes}} = {{a \cdot c_{V}^{3}} + {b \cdot c_{V}^{2}} + {c \cdot c_{V}} + d}}} & \left( {{Equation}\mspace{14mu} M} \right)\end{matrix}$

with:

-   -   η Hindrance function    -   v Measured speed    -   v_(Stokes) Sink speed according to Equation 5    -   c_(v) Volume concentration    -   a, b, c, d Factors for the adjustment to the experimental data

The following fit parameters were computed for the example above(stability index 0.9920):

a=−379 b=112 c=−13.21 d=1

FIG. 3 represents the hindrance function (measured values and adjustmentequation) depending on the concentration of solid substance, and showsthe good correlation of the experimental values (symbols) with thecalculated values (line).

On the basis of the equation above, the hindrance function necessary forthe calculation of the grain size for concentrated dispersions can becomputed for any volume concentrations. In addition, the relativeconcentration-dependent viscosity can be calculated by dividing(1−c_(v))² by η(c_(v)) (Equation M1).

$\begin{matrix}{{\mu \left( c_{V} \right)} = {\frac{\left( {1 - c_{V}} \right)^{2}}{\eta \left( c_{V} \right)} = \frac{\left( {1 - c_{V}} \right)^{2}}{{a \cdot c_{V}^{3}} + {b \cdot c_{V}^{2}} + {c \cdot c_{V}} + d}}} & \left( {{Equation}\mspace{14mu} {M1}} \right)\end{matrix}$

Using Equation M, the flux density function Φ(c_(v)) can also becalculated for any volume concentrations corresponding to Equation M2.

Φ(c _(v))=c _(v)·η(c _(v))=a·c _(v) ⁴ +b·c _(v) ³ +c·c _(v) ² +d·c_(v)  (Equation M2)

EXEMPLARY EMBODIMENT 4 Determination of the Distribution of Particlesizes of a Latex Sample Evaluated Based on Volume

In this example, the distribution of grain sizes for a polydisperselatex sample was calculated from position-dependent extinction profilesat different times t and from the time-dependent extinction at differentestablished position ranges (r+δr) for the cuvettes.

Preparation of samples: The original samples were stirred up and dilutedwith 1% sodium dodecyl sulfate to a solid substance concentration of3.5% m/m latex, and then poured into the cuvettes made of polycarbonate(2.2 mm layer thickness). The net weight amounted to approximately 0.47g.

Experiment: The centrifugal analysis was carried out with 2 samples atthe same time (parallel determinations) at a rotor speed of a constant4000 revolutions per minute (corresponding to 2300 times theacceleration of gravity). The temperature during the test amounted to aconstant 25° C. The centrifugation time amounted to approximately 14hours at a measurement reading interval of 150 seconds.

A conversion of the measured transmission values T(r, t) into extinctionvalues E(r, t) was necessary for the data analysis. The experimentallydetermined transmission values for the samples are to be corrected forit corresponding to Equation N with respect to the transmission for thecuvettes filled only with the dispersion medium T₀(r) (blank value,determined for the same cuvettes in a prior experiment or for a cuvetteconstructed in the same way in the same course).

$\begin{matrix}{{E\left( {r,t} \right)} = {- {\ln \left( \frac{T\left( {r,t} \right)}{T_{0}(r)} \right)}}} & \left( {{Equation}\mspace{14mu} N} \right)\end{matrix}$

On the one hand, the determination of the cumulative distribution ofparticle sizes takes place on the basis of the ascertainment of the massfraction for the particle fraction, which has already completelyprecipitated out of the sample at various points in time at which thetransmission was measured. As an example, the temporal courses of theextinctions averaged over the rotor positions first from 114.5 to 115.5mm, second from 120.5 to 120.5 mm and third from 124.5 to 125.5 mm wereused for the analysis. With the help of the Equations O through Q, thecumulative distribution of particle sizes Q₃(x) was calculated at thepositions 115 mm, 120 mm and 125 mm.

$\begin{matrix}{c_{V} = {c_{V,0} \cdot {\int_{x_{\min}}^{x}{{{\exp\left( \frac{\begin{matrix}{{- 2} \cdot \left( {\rho_{P} - \rho_{F}} \right) \cdot} \\{\omega^{2} \cdot t \cdot z^{2}}\end{matrix}}{18 \cdot \mu_{C}} \right)} \cdot {q_{3}(z)}}\ {z}}}}} & \left( {{Equation}\mspace{14mu} O} \right)\end{matrix}$

E=A _(v) ·c _(v) ·L  (Equation P)

dQ ₃(x)=q ₃(x)·dx  (Equation Q)

with:

-   -   Q₃(x) Cumulative distribution of particle sizes weighted by        volume    -   q₃(x) Differential distribution of particle sizes weighted by        volume    -   A_(v)(x) Volume-specific extinction cross section    -   x Particle size    -   E Extinction    -   r Position    -   t Time    -   c_(v) Volume concentration    -   μc Viscosity of the dispersion medium 0.899 mPa s    -   ρ_(P) Density of the dispersed substance 1.23 g/cm³    -   ρ_(F) Density of the dispersion medium 0.998 g/cm³    -   L Optical path length 2.2 mm    -   ω Angular speed 419 l/s

On the other hand, the radial dependency of the extinction at the timest=1023 s, t=1526 s, t=2029 s, t=2532 s and t=3035 s were used in orderto calculate the cumulative distribution of particle sizes with thefollowing equation R.

$\begin{matrix}{{Q_{3}\left( {x\left( {r,t} \right)} \right)} = \frac{\int_{E_{\min}}^{E{(r)}}{\frac{r^{2}}{A_{V}\left( {x\left( {r,t} \right)} \right)}\ {{E(r)}}}}{\int_{E_{\min}}^{E_{\max}}{\frac{r^{2}}{A_{V}\left( {x\left( {r,t} \right)} \right)}\ {{E(r)}}}}} & \left( {{Equation}\mspace{14mu} R} \right)\end{matrix}$

with:

-   -   Q₃(X) Cumulative distribution of particle sizes weighted by        volume    -   A_(v)(x) Volume-specific extinction cross section    -   x Particle size    -   E Extinction    -   r Position    -   t Time

The diameter of the particles x, which have already passed all of therotor positions r at the time t, was calculated on the basis of EquationS.

$\begin{matrix}{{x\left( {r,t} \right)} = \sqrt{\frac{18 \cdot \mu_{C}}{\left( {\rho_{P} - \rho_{F}} \right) \cdot \omega^{2} \cdot t} \cdot {\ln \left( \frac{r}{r_{0}} \right)}}} & \left( {{Equation}\mspace{14mu} S} \right)\end{matrix}$

with:

-   -   ρ_(p) Density of the dispersed substance 1.23 g/cm³    -   ρ_(F) Density of the dispersion medium 0.998 g/cm³    -   μ_(c) Viscosity of the dispersion medium 0.899 mPa s    -   x Particle size    -   ωAngular speed 419 l/s    -   r Position    -   r₀ Position of the fill level    -   t Time

Ideally, all calculated distribution functions must fall one upon theother. The diagram in FIG. 4, in which the cumulative distributions ofparticle sizes Q(x) are plotted over the particle size x for thepositions r=115 mm, 120 mm, 125 mm (symbols) and the times t=1023 s,1526 s, 2029 s, 2535 s, 3035 s (lines), shows the very good correlationof all calculated distributions.

EXEMPLARY EMBODIMENT 5 Determination of the Particle DensityDistribution of a Pearl Cellulose Sample in the Gravitation Field

In this example, the cumulative distribution of the particle density ofa pearl cellulose sample characterised by an average porosity wasdetermined from the segregation kinetics in the gravitation field. Theparticle diameter amounts to 40 μm.

Preparation of samples: The sample was placed in a beaker and thenstirred for 10 minutes by means of a magnetic stirrer. Then thesuspension was filled into the plastic cuvettes (2.2 mm film thickness)such that 99 mg of solid substance was obtained. The cuvette was thentopped off to 504 mg of suspension with water, and shaken immediatelyprior to the start of the test in order to ensure that the sample isevenly stirred.

Experiment: The segregation analysis in the gravitation field wascarried out at a temperature of 24.5° C. over a period of 255 times 14seconds. At the same time, the transmission profiles were recorded in arange of 55 mm. The position of the fill level amounted to h_(o)=22.1 mmand the position of the bottom of the cuvette amounted to 48.8 mm.

A conversion of the measured transmission values T(h, t) into extinctionvalues E(h, t) was necessary for the data analysis. The experimentallydetermined transmission values for the samples are to be corrected forit corresponding to Equation T with respect to the transmission for thecuvettes T_(cell)(h) filled only with the dispersion medium (blankvalue).

$\begin{matrix}{{E\left( {h,t} \right)} = {- {\ln \left( \frac{T\left( {h,t} \right)}{T_{cell}(h)} \right)}}} & \left( {{Equation}\mspace{14mu} T} \right)\end{matrix}$

The position-dependent course of the extinction at the time t E(r, t)was used in order to calculate the cumulative distribution of theparticle density according to the following Equation U.

$\begin{matrix}{{Q\left( \rho_{P} \right)} = \frac{E\left( {h,t} \right)}{E_{\max}(t)}} & \left( {{Equation}\mspace{14mu} U} \right)\end{matrix}$

with:

-   -   Q(ρ_(P)) Cumulative distribution of the particle density    -   E(h,t) Extinction at the position h at time t    -   E_(max)(t) Maximum extinction at time t

This approach is only valid as long as the extinction coefficient is nota function of the particle density. The substance system contemplated inthis example fulfills this condition sufficiently

The particle density ρ_(P)(h, t) of the particles, which have alreadypassed the position h, was calculated on the basis of Equation V.

$\begin{matrix}{{\rho_{P}\left( {h,t} \right)} = {\rho_{F} + \frac{18 \cdot \left( {h - h_{0}} \right) \cdot \mu_{C}}{g \cdot x^{2} \cdot t}}} & \left( {{Equation}\mspace{14mu} V} \right)\end{matrix}$

with:

-   -   ρ_(P) Density of the dispersed substance    -   ρ_(F) Density of the dispersion medium 0.997 g/cm³    -   μ_(c) Viscosity of the dispersion medium 0.910 mPa s    -   x Particle size 4 μm    -   g Acceleration of gravity 9.81 m/s²    -   h Position    -   h₀ Position of the fill level 22.1 mm    -   t Time 14 s

FIG. 5 shows the calculated cumulative distribution of the particledensity at the time t=14 s for the porous pearl cellulose. Cellulosegenerally has a solid substance density of 1.5 g/cm³. This valuenaturally forms the upper limit of the density distribution, because theeffective density results as an average of the solid substance densityand of the water located in the pores.

LEGEND FOR THE FIGURES

FIG. 1 shows the equalising function for the extinction coefficientsdetermined for Sample A.

FIG. 2 compares the results of the reference measurement with theexperimentally determined values for Sample B.

The comparison of the experimental hindrance function (symbols) with thecalculated hindrance function (line) is shown in FIG. 3.

The cumulative distributions of particle sizes Q(x) are to be discernedin FIG. 4 for the positions r=115 mm, 120 mm, 125 mm (symbols) and thetimes t=1023 s, 1526 s, 2029 s, 2535 s, 3035 s (lines).

FIG. 5 shows the cumulative distribution of the particle density for theporous pearl cellulose determined from the transmission profile recordedat the time t=14 s.

1. Method for the automatic determination of selected physical,technical method and colloidal chemistry parameters (for example, thegrain size, the distribution of grain sizes, the speed distribution, theparticle flux, the hindrance function and indices of structuralstability) by means of the determination of the attenuation of radiatedwaves during the segregation of monodisperse or polydisperse dispersionsamples subjected to gravitation or centrifugation, characterised by thefollowing features: during the segregation by means of centrifugation orgravitation, the momentary transmission I_(T)(t, r) characterising thecurrent segregation status of the waves radiated with the intensityI_(o)(t, r) and/or the instantaneous scattering I_(S)(t, r) as afunction of the position within the samples is repeatedly determined andrecorded at high resolution at any arbitrary time for one or morewavelengths over the entire length of the sample or in selected partialsections of it, simultaneously for multiple and even concentratedsamples with known and/or unknown physical and colloidal chemistryproperties. the extinction profile E_(T)(t, r) is calculated by findingthe log of the ratio of I_(o)(t, r)/I_(T)(t, r) for the determination ofthe particle or droplet concentration for the tested dispersion samplesas a function of sample position and time. from these extinctionprofiles E_(T)(t, r) determined at different times (t1 . . . tn) and thelocal adjustment made in these time segments (t(n−1)−t(n)), segregationspeeds are calculated for any constant extinction values. from the ratioof the segregation speeds determined for specific extinctionpercentiles, a polydispersity index is calculated, which ischaracteristic for the polydispersity of the density or the particle ordroplet size. extinction-weighted distributions of the grain size arecalculated from extinction profiles E_(T)(t, r) for selectable timesaccording to Equation A while standardising on the maximum extinctionfor this profile. the local and temporal change of the particle ordroplet concentration can be determined by taking into account thesubstance-specific extinction concentration relationship. thesubstance-specific extinction-concentration relationship is calculatedthrough the simultaneous segregation of samples of the substance systemto be measured with known, varying volume concentrations, whereby theconcentration effect on the extinction is calculated while taking intoaccount the repeated scattering, for example according to Equation Band/or the volume-weighted distributions of the grain size arecalculated according to Equations A and C from any extinction profilesacquired at time t according to 1.2, whereby the volume-specificextinction cross section that is dependent on particle size and that isrequired for doing so is calculated according to Mie while including thedevice constants from the known optical substance parameters, or as analternative to 1.8.1, the method allows the experimental determinationof the volume-specific extinction cross section that is dependent onparticle size if the extinction of at least two monodisperse referencesamples is determined corresponding to 1.2, or as an alternative to1.8.1, the method allows the experimental determination of thevolume-specific extinction cross section that is dependent on particlesize if the course of the extinction is determined during thesegregation of at least one polydisperse substance system with similaroptical characteristics corresponding to 1.2 and/or using thevolume-weighted distribution of particle sizes determined in 1.8, theparticle size dependency for the volume-specific extinction crosssection determined in 1.8.1-1.8.3, and the concentration-dependentextinction determined in item 1.6, each radial position and the particlesize associated with it via Equation A is assigned a volumeconcentration corresponding to Equation D and/or the flux densityfunction standardised to the centrifugation constant (Equation F) isdetermined from the change in the concentration of the samples withknown starting concentration and/or the concentration-dependenthindrance function for the substance system is determined correspondingto Equations E, E* and F and/or the volume-weighted distribution of theStokes equivalent diameter for the case of hindrance functions not equalto 1 is determined by iteratively repeating Equation G instead ofEquation A for the steps described in 1.2 through 1.11 until thedifference between the concentration profiles of consecutive steps areless than a value to be provided in advance, or if the allowance for thehydrodynamic impediment (Equation E) is provided by means of anothersuitable mathematical algorithm, for example via the definition of acost function.
 2. Method according to claim 1, wherein the determinationof the grain sizes and their distribution is possible for dispersedparticles with density both greater as well as less than that of thedispersion medium.
 3. Method according to claim 1, wherein in place ofthe position-dependent extinction profile E_(T)(t, r) at time t, theextinction is determined as a function at a freely selectable positionor over a range (r+δr) of the sample, and the distribution of grainsizes is calculated from it analogously to the above calculation. 4.Method according to claim 1, wherein the apparent relative viscosity canbe calculated as a function of the concentration by volume from thehindrance function taking into account the concentration by volume. 5.Method according to claim 1, wherein the sedimentation type and thecritical concentration by volume for the use of consolidation phenomenacan be determined from the change in the segregation speed during thesegregation.
 6. Method according to claim 1, wherein the ascertainablerange of the distribution of sizes as well as the resolution withrespect to the distribution of grain sizes can be increased by varyingthe number of revolutions and the measurement time intervals.
 7. Methodaccording to claim 1 wherein the mass density distribution of the sampleis calculated from the extinction profile E_(T)(t, r) for a knowndistribution of grain sizes.
 8. Method according to claim 1 wherein formixtures of substances of different densities, the distribution of grainsizes for the individual substance components is calculated from theextinction profiles for the segregation of dispersions with differentdensities for the dispersion medium.
 9. Method according to claim 1,wherein indices for the consolidation behavior of the dispersion samplescan be computed from the sediment levels for gradually changedrevolutions related to the respective operative centrifugal force. 10.Method according to claim 1 wherein the control of the segregationanalyser and the measurement sensor, including radiation source, samplemanagement and data transfer, data handling and data storage, as well asall steps of analysis and the documentation of the results, takes placeby means of software supported by a database.
 11. Device for theautomatic determination of selected physical, technical method andcolloidal chemistry parameters (for example, the grain size, thedistribution of grain sizes, the speed distribution, the particle flux,the hindrance function and indices of structural stability), consistingof a PC-controlled multi-sample receptacle unit arranged vertically orhorizontally with a spectrometric measurement device with a sourceproducing monochromatic parallel radiation, which registers, digitisesand stores the radiation intensity scattered or transmitted by therespective dispersion sample over the entire length of the samplesimultaneously or shifted temporally during the segregation, resolvedfor location and time.
 12. Device according to claim 11, whereindifferent cuvettes matched to the measurement task and/or the dispersionsample with respect to the optical path length and the materials can beused, the cuvette type is detected automatically, and the parametersrequired for the analysis of the measurement results are automaticallymade available via database entries for the calculation of theparameters to be analysed.
 13. Device according to claim 11 whereinradiation sources of different monochromatic wavelengths, whoseradiation intensity I_(o)(t, r) can be varied, are also used electivelyin an alternating fashion, depending on the sample and measurementtasks.
 14. Device according to claim 11 wherein the measurement rangecan be controlled by thermostat and the measurements can be carried outat selectable temperatures both under as well as over room temperature.15. Device according to claim 11 wherein the multi-sample receptacleunit is designed as a rotor, and is driven by a motor with programmablevariable and/or constant revolutions.
 16. Device according to claim 11,has a multi-sample receptacle unit, which makes possible the acceptanceof samples placed vertically for segregation in the gravitational field.